We studied the worldwide distribution of personality traits on the basis of a mathematical model based on Mendelian genetics. The model consists of three traits, each assumed to be the expression of a pleiotropic gene, namely: sanguinity, perfectionism and aggression. Presence or absence of the three traits gives rise to discrete personality types. The model implicitly incorporates relative infertility of certain combinations of the types and is found to be consistent with the concept of Dobzhansky-Muller hybrid inviability. The model predicts stable polymorphisms of the character phenotypes that could be analyzed with the use of the classical Hardy-Weinberg concepts of gene frequencies and populations in equilibrium. Both indigenous and non-indigenous groups around the world were typed according to the three traits with the use of archival sources and information available on the internet. Attention was given to the Australian Aborigines, for which more than a hundred, mostly isolated and remote communities were typed. Our results are presented in the form of color-coded maps that depict the worldwide distribution of the character phenotypes and the three traits. The results are discussed with respect to the "Out of Africa" concept of the ancestral migrations of modern humans.